Overcoming resolution limits with quantum sensing

Manipulation of path state based on spatiotemporal dielectric metasurface

In this work, a spatiotemporal metasurface is proposed to manipulate the path of photons flexibly. The spatial modulation is induced by the rectangle silicon units aligned on silica in a manner with a phase gradient only for y-polarized photons, and the temporal modulation is contributed by the pumps of constructing Kerr dynamic gratings. By quantizing designed metasurfaces, the analytical solutions of output photon states can be derived correspondingly. Reversal design could be implemented by tailoring the profile of higher harmonics to infer the intensity of pumps, size of meta-atoms, and initial state. The path-polarization entanglement and correlations of output photons are realized, and then a CNOT gate is obtained by utilizing the deflection of the photon path. This work provides a scheme to deal with the spatiotemporal metasurfaces and expands the applications of metasurfaces in the quantum realm.

Optimal Sensing Protocol for Statistically Polarized Nano-NMR with NV Centers

Diffusion noise represents a major constraint to successful liquid state nano-NMR spectroscopy. Using the Fisher information as a faithful measure, we theoretically calculate and experimentally show that phase sensitive protocols are superior in most experimental scenarios, as they maximize information extraction from correlations in the sample. We derive the optimal experimental parameters for quantum heterodyne detection (Qdyne) and present the most accurate statistically polarized nano-NMR Qdyne detection experiments to date, leading the way to resolve chemical shifts and J couplings at the nanoscale.

Gradient-Descent Quantum Process Tomography by Learning Kraus Operators

We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive. To make the process trace preserving, we use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. Our ansatz uses a few Kraus operators to avoid direct estimation of large process matrices, e.g., the Choi matrix, for low-rank quantum processes. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes, but shines by combining the best features of these two methods. Similar to CS (but unlike PLS), GD-QPT can reconstruct a process from just a small number of random measurements, and similar to PLS (but unlike CS) it also works for larger system sizes, up to at least five qubits. We envisage that the data-driven approach of GD-QPT can become a practical tool that greatly reduces the cost and computational effort for QPT in intermediate-scale quantum systems.

High field magnetometry with hyperpolarized nuclear spins

Quantum sensors have attracted broad interest in the quest towards sub-micronscale NMR spectroscopy. Such sensors predominantly operate at low magnetic fields. Instead, however, for high resolution spectroscopy, the high-field regime is naturally advantageous because it allows high absolute chemical shift discrimination. Here we demonstrate a high-field spin magnetometer constructed from an ensemble of hyperpolarized ¹³C nuclear spins in diamond. They are initialized by Nitrogen Vacancy (NV) centers and protected along a transverse Bloch sphere axis for minute-long periods. When exposed to a time-varying (AC) magnetic field, they undergo secondary precessions that carry an imprint of its frequency and amplitude. For quantum sensing at 7T, we demonstrate detection bandwidth up to 7 kHz, a spectral resolution < 100mHz, and single-shot sensitivity of 410pT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$/\sqrt{{{{{{{{\rm{Hz}}}}}}}}}$$\end{document}/Hz. This work anticipates opportunities for microscale NMR chemical sensors constructed from hyperpolarized nanodiamonds and suggests applications of dynamic nuclear polarization (DNP) in quantum sensing.

Quantum sensors based on NV centers in diamond find applications in high spatial resolution NMR spectroscopy, but their operation is typically limited to low fields. Sahin et al. demonstrate a high-field sensor based on nuclear spins in diamond, where NV centers play a supporting role in optical initialization.

Record Chemical-Shift Temperature Sensitivity in a Series of Trinuclear Cobalt Complexes

Designing spins that exhibit long-lived coherence and strong temperature sensitivity is central to designing effective molecular thermometers and a fundamental challenge in the chemistry/quantum-information space. Herein, we provide a new pathway to both properties in the same molecule by designing a nuclear spin, which possesses a robust spin coherence, to mimic the strong temperature sensitivity of an electronic spin. This design strategy is demonstrated in the group of trinuclear Co(III) spin-crossover compounds [(CpCo(OP(OR)₂)₃)₂Co](SbCl₆) where Cp = cyclopentadienyl and R = Me (1), Et (2), i-Pr (3), and t-Bu (4). Nuclear magnetic resonance analyses of the ⁵⁹Co nuclear spins reveal ⁵⁹Co chemical-shift temperature sensitivity (Δδ/ΔT) values that span from 101(1) ppm/°C in 1 to 149(1) ppm/°C in 2 and 150(2) ppm/°C in 4, where the latter two are record temperature sensitivities for any nuclear spin. Additionally, complexes 2 and 4 have T₂^* values of 74 and 78 μs in solution at ambient temperatures surpassing those from electron-spin-based complexes, which typically display long coherence times only at extremely low temperatures. Our results suggest that spin-crossover phenomena can enable electron-spin-like temperature sensitivities in nuclear spins while retaining robust coherence times at room temperature.

Variational Principle for Optimal Quantum Controls in Quantum Metrology

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios.

Entangled Photon Spectroscopy

The enhanced interest in quantum-related phenomena has provided new opportunities for chemists to push the limits of detection and analysis of chemical processes. As some have called this the second quantum revolution, a time has come to apply the rules learned from previous research in quantum phenomena toward new methods and technologies important to chemists. While there has been great interest recently in quantum information science (QIS), the quest to understand how nonclassical states of light interact with matter has been ongoing for more than two decades. Our entry into this field started around this time with the use of materials to produce nonclassical states of light. Here, the process of multiphoton absorption led to photon-number squeezed states of light, where the photon statistics are sub-Poissonian. In addition to the great interest in generating squeezed states of light, there was also interest in the formation of entangled states of light. While much of the effort is still in foundational physics, there are numerous new avenues as to how quantum entanglement can be applied to spectroscopy, imaging, and sensing. These opportunities could have a large impact on the chemical community for a broad spectrum of applications.In this Account, we discuss the use of entangled (or quantum) light for spectroscopy as well as applications in microscopy and interferometry. The potential benefits of the use of quantum light are discussed in detail. From the first experiments in porphyrin dendrimer systems by Dr. Dong-Ik Lee in our group to the measurements of the entangled two photon absorption cross sections of biological systems such as flavoproteins, the usefulness of entangled light for spectroscopy has been illustrated. These early measurements led the way to more advanced measurements of the unique characteristics of both entangled light and the entangled photon absorption cross-section, which provides new control knobs for manipulating excited states in molecules.The first reports of fluorescence-induced entangled processes were in organic chromophores where the entangled photon cross-section was measured. These results would later have widespread impact in applications such as entangled two-photon microscopy. From our design, construction and implementation of a quantum entangled photon excited microscope, important imaging capabilities were achieved at an unprecedented low excitation intensity of 10⁷ photons/s, which is 6 orders of magnitude lower than the excitation level for the classical two-photon image. New reports have also illustrated an advantage of nonclassical light in Raman imaging as well.From a standpoint of more precise measurements, the use of entangled photons in quantum interferometry may offer new opportunities for chemistry research. Experiments that combine molecular spectroscopy and quantum interferometry, by utilizing the correlations of entangled photons in a Hong-Ou-Mandel (HOM) interferometer, have been carried out. The initial experiment showed that the HOM signal is sensitive to the presence of a resonant organic sample placed in one arm of the interferometer. In addition, parameters such as the dephasing time have been obtained with the opportunity for even more advanced phenomenology in the future.

Optical-domain spectral super-resolution via a quantum-memory-based time-frequency processor

Existing super-resolution methods of optical imaging hold a solid place as an application in natural sciences, but many new developments allow for beating the diffraction limit in a more subtle way. One of the recently explored strategies to fully exploit information already present in the field is to perform a quantum-inspired tailored measurements. Here we exploit the full spectral information of the optical field in order to beat the Rayleigh limit in spectroscopy. We employ an optical quantum memory with spin-wave storage and an embedded processing capability to implement a time-inversion interferometer for input light, projecting the optical field in the symmetric-antisymmetric mode basis. Our tailored measurement achieves a resolution of 15 kHz and requires 20 times less photons than a corresponding Rayleigh-limited conventional method. We demonstrate the advantage of our technique over both conventional spectroscopy and heterodyne measurements, showing potential for application in distinguishing ultra-narrowband emitters, optical communication channels, or signals transduced from lower-frequency domains.

Quantum Sensing of Thermoelectric Power in Low-Dimensional Materials

Thermoelectric power, has been extensively studied in low-dimensional materials where quantum confinement and spin textures can largely modulate thermopower generation. In addition to classical and macroscopic values, thermopower also varies locally over a wide range of length scales, and is fundamentally linked to electron wave functions and phonon propagation. Various experimental methods for the quantum sensing of localized thermopower have been suggested, particularly based on scanning probe microscopy. Here, critical advances in the quantum sensing of thermopower are introduced, from the atomic to the several-hundred-nanometer scales, including the unique role of low-dimensionality, defects, spins, and relativistic effects for optimized power generation. Investigating the microscopic nature of thermopower in quantum materials can provide insights useful for the design of advanced materials for future thermoelectric applications. Quantum sensing techniques for thermopower can pave the way to practical and novel energy devices for a sustainable society.

Quantum State Tomography with Conditional Generative Adversarial Networks

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.

Quantum Limits of Superresolution in a Noisy Environment

We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with noiseless cases where the quantum Fisher information has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution. In addition, we show that false excitation on an arbitrary measurement, such as dark counts, also makes the classical Fisher information of the measurement approach to zero as the separation goes to zero. Finally, a practically relevant situation resolving two identical thermal sources is quantitatively investigated by using the quantum and classical Fisher information of finite spatial mode multiplexing, showing that the amount of noise poses a limit on the resolution in a noisy system.

"Super-Heisenberg" and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field

The Heisenberg scaling, which scales as N^{-1} in terms of the number of particles or T^{-1} in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as "super-Heisenberg scaling," however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as T^{-1} and T^{-2}, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.

Correlated noise in Brownian motion allows for super resolution

Diffusion broadening of spectral lines is the main limitation to frequency resolution in non-polarized liquid state nano-NMR. This problem arises from the limited amount of information that can be extracted from the signal before losing coherence. For liquid state NMR as with most generic sensing experiments, the signal is thought to decay exponentially, severely limiting resolution. However, there is theoretical evidence that predicts a power law decay of the signal’s correlations due to diffusion noise in the non-polarized nano-NMR scenario. In this work we show that in the NV based nano-NMR setup such diffusion noise results in high spectral resolution.

Design of an on-Chip Room Temperature Group-IV Quantum Photonic Chem/Bio Interferometric Sensor Based on Parity Detection

We propose and analyze three Si-based room-temperature strip-guided "manufacturable" integrated quantum photonic chem/bio sensor chips operating at wavelengths of 1550 nm, 1330 nm, and 640 nm, respectively. We propose design rules that will achieve super-sensitivity (above the classical limit) by means of mixing between states of coherent light and single-mode squeezed-light. The silicon-on-insulator (SOI), silicon-on-sapphire (SOS), and silicon nitride-on-SiO2-on Si (SiN) platforms have been investigated. Each chip is comprised of photonic building blocks: a race-track resonator, a pump filter, an integrated Mach-Zehnder interferometric chem/bio sensor, and a photonic circuit to perform parity measurements, where our homodyne measurement circuit avoids the use of single-photon-counting detectors and utilizes instead conventional photodetectors. A combination of super-sensitivity with super-resolution is predicted for all three platforms to be used for chem/bio sensing applications.

Quantum Limits to Incoherent Imaging are Achieved by Linear Interferometry

We solve the general problem of determining, through imaging, the three-dimensional positions of N weak incoherent pointlike emitters in an arbitrary spatial configuration. We show that a structured measurement strategy in which a passive linear interferometer feeds into an array of photodetectors is always optimal for this estimation problem, in the sense that it saturates the quantum Cramér-Rao bound. We provide a method for the explicit construction of the optimal interferometer. Further explicit results for the quantum Fisher information and the optimal interferometer design that attains it are obtained for the special case of one and two incoherent emitters in the paraxial regime. This work provides insights into the phenomenon of superresolution through incoherent imaging that has attracted much attention recently. Our results will find a wide range of applications over a broad spectrum of frequencies, from fluorescence microscopy to stellar interferometry.